How do I subdivide all faces in a mesh equally?
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I know of a couple of options that will do what you're looking for.

The first is using sculpting like you're doing already. However, in the dynamic topology settings, there is a button called Detail Flood Fill. This applies the selected detail level to the whole object without having to manually sculpt.

Blender also has a modifier called Remesh. Add this modifier (second column about halfway down in the list of modifiers), set the mode to Smooth, and turn up the Octree Depth a bit.